SOLUTION: Toss the coin three times. If the coin lands either all heads or all tails, reject H0:p=1/2. (The p denotes the chance for the coin to land on heads.) (a) What is the probabili

Question 971749: Toss the coin three times. If the coin lands either all heads or all tails, reject H0:p=1/2. (The p denotes the chance for the coin to land on heads.)
(a) What is the probability of a Type I error for this procedure?
(b) If p = 3/4, what is the probability of a Type II error for this procedure?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
reject Ho when Ho is true. For all heads or tails it is (1/2)^3, so it is 0.25 altogether.
Accept Ho when it is false. Probability of all heads is 27/64 and all tails is (1/64). Everything else is 36/64. We are not rejecting a null hypothesis when we should, and the probability is 0.5625
Do a tree diagram
;;;;;;;;;3/4
3/4;; 3/4 ;;;1/4
;;;;1/4 ;;;3/4
;;;;;;;; 1/4

;;;1/4
1/4 ;;;;3/4 ;;;3/4
;;;;; 1/4 ;;;3/4
;;;;1/4

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